Signal-to-noise ratio, error and uncertainty of PIV measurement

Abstract

In particle image velocimetry (PIV) the measurement signal is contained in the recorded intensity of the particle image pattern superimposed on a variety of noise sources. The inherent amount of signal mutual information between consecutive images governs the strength of the resulting PIV cross correlation and ultimately the accuracy and uncertainty of the produced PIV measurements. Hence we posit that correlation signal-to-noise-ratio (SNR) metrics calculated from the correlation plane can be used to quantify the quality of the correlation and the resulting uncertainty of an individual measurement. In this paper we present a framework for evaluating the correlation SNR using a set of different metrics, which in turn are used to develop models for uncertainty estimation. A new SNR metric termed “mutual information” (MI) which quantifies the amount of common information (particle pattern) between two consecutive images is also introduced and investigated. This measure provides a direct estimation of the apparent NIFIFO parameter of an image pair providing an alternative approach towards uncertainty estimation but also connecting the current development to one of the most fundamental principles of PIV and the previously established theory. The SNR metrics and corresponding models presented herein are expanded to be applicable to both standard and filtered correlations and the notion of “valid” measurement is redefined with respect to the correlation peak width. These advancements lead to more robust uncertainty estimation models, which are tested against both synthetic benchmark data as well as actual experimental measurements. For all cases considered here, expanded uncertainties are estimated at the 95% confidence level, and the resulting calculated coverages are approximately 95% thus demonstrating the feasibility and applicability of these new models for direct estimation of uncertainty for individual PIV measurements.